Affiliation:
1. Department of Mathematics and Programming Technologies Francisk Skorina Gomel State University Sovietskaya, Gomel Belarus
2. Regional Mathematical Center Southern Federal University Rostov‐on‐Don Russia
Abstract
AbstractNecessary and sufficient conditions are given for the boundedness of Hausdorff operators on the generalized Hardy spaces , real Hardy space , , and for compact Abelian group G. Surprisingly, these conditions turned out to be the same for all groups and spaces under consideration. Applications to Dirichlet series are given. The case of the space of continuous functions on G and examples are also considered.